Abstract
For a wide class of Banach spaces of complex sequences, multiplier representations are given. If Lip(E, ∝) is a Banach space of sequences of Fourier coefficients of distributions in a Lipschitz space of order ∝ and VE is a Banach space of sequences of Fourier coefficients of distributions of generalized bounded variation, then these representations lead to extensions to Lip (E ∝) and VE of theorems of Privalov (on the conjugate invariance of Lip∝ (0<∝<l)), of Bernstein (on the absolute convergence of Fourier series of fe Lip (L2π,α),(∝>1/2)) and of Zygmund (on the absolute convergence of Fourier series of fε BV2π ∩ Lip∝, (∝>0)).
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© 1978 Birkhäuser Verlag Basel
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Goes, G. (1978). Multiplier Representations of Sequence Spaces with Applications to Lipschitz Spaces and Spaces of Functions of Generalized Bounded Variation. In: Butzer, P.L., Szökefalvi-Nagy, B. (eds) Linear Spaces and Approximation / Lineare Räume und Approximation. International Series of Numerical Mathematics / Intermationale Schriftenreihe zur Numberischen Mathematik / Sùrie Internationale D’analyse Numùruque, vol 40. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7180-8_22
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DOI: https://doi.org/10.1007/978-3-0348-7180-8_22
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